TRMM: The Tropical Rainfall Measuring Mission
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A second difficulty associated with the small spatial scale of rain variations is the so-called
"beam-filling" problem. The horizontal extent of a typical vigorous thunderstorm cell is of
order 5 km, and the area of active updrafts producing most of the rain within this cell may be
smaller, perhaps 1 km in extent. Since the TRMM instruments all have footprints larger than
this, only part of the area covered by a TRMM pixel will in general be raining at any time.
The radiance measured by a TRMM instrument will thus be a combination of signals from
raining and non-raining areas, weighted in an unknown fashion. For a given instrument and
wavelength, the retrieval algorithm must take this subpixel variability into account in order
not to make a biased precipitation estimate (cf. Rosenfeld et al., 1992). The problem becomes
worse when multichannel algorithms for a single instrument such as TMI, or multi-instrument
(TMI-PR, TMI-VIRS) algorithms, are considered, because different instruments and different
TMI channels have different size footprints, and so no two observe exactly the same raining
scene.
There is no completely satisfactory way to eliminate the beam-filling problem. The most useful
strategy is to use models of precipitating cloud systems to simulate the radiance seen by the
spacecraft at various resolutions under different raining conditions (Smith et al., 1991; Adler
et al., 1992), and to validate algorithms developed in this way against ground-based estimates
of precipitation on smaller spatial scales. This requirement thus dictates the need for TRMM
to include a substantial "ground-truth" validation program. We will return to this subject in
Section 20.6.
20.4 Rain Retrieval Using TRMM Instruments
In-depth discussions of passive microwave (Simmer, 1996) and radar (Joe, 1996) retrieval techniques for precipitation are presented elsewhere in this volume. In this section I simply present
an overview of the principles underlying active and passive remote sensing of rain as they apply
to instruments on TRMM (see also Simpson, 1988). Additional information on recent developments in remote rainfall estimation algorithms can be found in the special February 1993 issue
of Journal of Applied Meteorology.
20.4.1 Precipitation Radar (PR)
The estimation of rainfall by surface-based radars is one of the most widespread applications of
remote sensing in existence. The requirement for surface rain radars i's that they operate at a
sufficiently long wavelength (typically> 5 cm) so that attenuation of the beam by rain droplets
is insignificant. Under such circumstances a relationship between the radar reflectance Z and
the rainfall rate R exists, taking the form Z = aRb, where a and b are empirically determined
constants. One immediate problem for a spaceborne radar algorithm is that the constants vary
regionally, because Z is a strong function of the droplet size distribution (proportional to D 6 ,
where D is the droplet diameter). Thus, a single Z-R relationship valid for rain in different
parts of the tropics may not be feasible.
A larger problem is that to get satisfactory resolution from space, a long wavelength radar
would require unacceptably large antenna dimensions. For space applications, then, a shorter
wavelength (2.16 em) radar is being used by TRMM. Z-R relationships can thus only be used
by TRMM in light rain situations, where attenuation is small. At higher rain rates, the TRMM
PR will instead make use of the information contained in the attenuation of the beam to derive
rain rates. The general concept is as follows: If the attenuation coefficient k (attenuation
per unit rain rate and distance through the raining layer) is approximately constant, then the
555
A second difficulty associated with the small spatial scale of rain variations is the so-called
"beam-filling" problem. The horizontal extent of a typical vigorous thunderstorm cell is of
order 5 km, and the area of active updrafts producing most of the rain within this cell may be
smaller, perhaps 1 km in extent. Since the TRMM instruments all have footprints larger than
this, only part of the area covered by a TRMM pixel will in general be raining at any time.
The radiance measured by a TRMM instrument will thus be a combination of signals from
raining and non-raining areas, weighted in an unknown fashion. For a given instrument and
wavelength, the retrieval algorithm must take this subpixel variability into account in order
not to make a biased precipitation estimate (cf. Rosenfeld et al., 1992). The problem becomes
worse when multichannel algorithms for a single instrument such as TMI, or multi-instrument
(TMI-PR, TMI-VIRS) algorithms, are considered, because different instruments and different
TMI channels have different size footprints, and so no two observe exactly the same raining
scene.
There is no completely satisfactory way to eliminate the beam-filling problem. The most useful
strategy is to use models of precipitating cloud systems to simulate the radiance seen by the
spacecraft at various resolutions under different raining conditions (Smith et al., 1991; Adler
et al., 1992), and to validate algorithms developed in this way against ground-based estimates
of precipitation on smaller spatial scales. This requirement thus dictates the need for TRMM
to include a substantial "ground-truth" validation program. We will return to this subject in
Section 20.6.
20.4 Rain Retrieval Using TRMM Instruments
In-depth discussions of passive microwave (Simmer, 1996) and radar (Joe, 1996) retrieval techniques for precipitation are presented elsewhere in this volume. In this section I simply present
an overview of the principles underlying active and passive remote sensing of rain as they apply
to instruments on TRMM (see also Simpson, 1988). Additional information on recent developments in remote rainfall estimation algorithms can be found in the special February 1993 issue
of Journal of Applied Meteorology.
20.4.1 Precipitation Radar (PR)
The estimation of rainfall by surface-based radars is one of the most widespread applications of
remote sensing in existence. The requirement for surface rain radars i's that they operate at a
sufficiently long wavelength (typically> 5 cm) so that attenuation of the beam by rain droplets
is insignificant. Under such circumstances a relationship between the radar reflectance Z and
the rainfall rate R exists, taking the form Z = aRb, where a and b are empirically determined
constants. One immediate problem for a spaceborne radar algorithm is that the constants vary
regionally, because Z is a strong function of the droplet size distribution (proportional to D 6 ,
where D is the droplet diameter). Thus, a single Z-R relationship valid for rain in different
parts of the tropics may not be feasible.
A larger problem is that to get satisfactory resolution from space, a long wavelength radar
would require unacceptably large antenna dimensions. For space applications, then, a shorter
wavelength (2.16 em) radar is being used by TRMM. Z-R relationships can thus only be used
by TRMM in light rain situations, where attenuation is small. At higher rain rates, the TRMM
PR will instead make use of the information contained in the attenuation of the beam to derive
rain rates. The general concept is as follows: If the attenuation coefficient k (attenuation
per unit rain rate and distance through the raining layer) is approximately constant, then the